The Tower of Babel in the Classroom?

Immigrants and Natives in Italian Schools

Rosario M. Ballatore 1 Margherita Fort 2 Andrea Ichino 3

1Bank of Italy2University of Bologna, CESifo and IZA

3EUI & University of Bologna, CEPR, CESifo and IZA

Workshop on Human Capital

Bank of Italy

Rome, November 29th, 2016

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Research question

The causal effect on school performance of a change in the

ethnic composition of a class due to an immigrant inflow

net of:

the endogenous adjustments of class size and students’ quality

generated by principals’ reactions to this inflow

We call it the Pure Ethnic Composition (PEC) effect

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Research question

The causal effect on school performance of a change in the

ethnic composition of a class due to an immigrant inflow

net of:

the endogenous adjustments of class size and students’ quality

generated by principals’ reactions to this inflow

We call it the Pure Ethnic Composition (PEC) effect

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Research question

The causal effect on school performance of a change in the

ethnic composition of a class due to an immigrant inflow

net of:

the endogenous adjustments of class size and students’ quality

generated by principals’ reactions to this inflow

We call it the Pure Ethnic Composition (PEC) effect

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Research question

The causal effect on school performance of a change in the

ethnic composition of a class due to an immigrant inflow

net of:

the endogenous adjustments of class size and students’ quality

generated by principals’ reactions to this inflow

We call it the Pure Ethnic Composition (PEC) effect

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Research question: the PRF

Vj = α + βNj + γIj + λQnj + µQ i

j + εj (1)

The effects of changing class size by varying the number of natives(immigrants) keeping immigrants (natives) constant for given qualityof the two ethnicities:

β =

(dVj

dN

)Ij=I;Qn

j =Qn;Qij=Qi

γ =

(dVj

dI

)Nj=N;Qn

j =Qn;Qij=Qi

(2)

The PEC effect is then given by

δ =

(dVj

dI

)Cj=C ;Qn

j =Qn;Q ij =Q i

= γ − β (3)

and is the effect of increasing exogenously the number of immigrantskeeping class size constant (i.e. reducing natives at the same time ).

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This paper in a nutshell

We explore features of the institutional setting:

rules of class formation (with a cap of 25 students per class)

Ministry of Education instructions to allocate immigrants wherethere is more space for them (e.g. where classes are smaller)

differences in enrolment between February (pre-enrolment) andSeptember (final enrolment)

the interaction between these features allows us to compare classes:

that have different numbers of natives and immigrants

for given students’ quality

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Main findings

The Pure Ethnic Composition (PEC) effect on native performance

is negative and statistically significant at age 7

≈ -1.6% for both language and math

it does not vanish when children grow up to age 10

When we use instead a more conventional identification strategy

our estimates of the effects of immigrant inflows on native

performance are smaller

because they are confounded by the endogenous

adjustments implemented by principals

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The data

We use INVALSI data for Italian primary schools in 2009-10.

For each student in grades 2 and 5 the data set contains:

test scores in language and mathematics

educational institution, school, grade, class and student identifiers

class size and class composition at the beginning of the year

immigrant status based parents’ nationality

some individual and family background information

The unit of analysis is the class

We restrict the analysis to

educational institutions with immigrants and more than one school

(80% of the students)

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Descriptive statistics for the language sample2nd grade 5th grade

Mean S.D. Mean S.D.Fraction of correct answers:- language (natives) 0.67 0.11 0.71 0.08- mathematics (natives) 0.61 0.11 0.65 0.10- language (immigrants) 0.53 0.19 0.60 0.15- mathematics (immigrants) 0.54 0.16 0.58 0.16

Number of natives in class 16.37 4.09 16.65 4.02Number of immigrants in class 3.08 2.21 3.02 2.17Class size 19.44 3.84 19.67 3.89

Sample size (number of classes) 12,859 13,084Sample size (number of schools) 7,387 7,496Sample size (number of institutions) 2,734 2,776

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Identification: institutional framework

In February

Students should pre-enrol in a given school for the year that starts inthe following September

The number of classes are tentatively formed by principals according tonatives pre-enrolment, following a “Maimonides-type rule” with a capat 25

The Ministry of Education instructs principals to put immigrants in theschools where, depending on natives enrolment, classes are smaller

In September

Additional splitting of classes occurs in September if late enrolmentrequires any further adjustment

No more room for endogenous reaction of principals

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An example

Consider grade g of school s.

Predicted class size CNsg , based on native pre-enrolment and rules of

class formation, can take three equally likely values:

H > M > L =H

2.

The principal knows that

if CNsg = H in February, with probability π that class will be split in

September

splitting will originate two classes each one with (approximately)L = H

2 natives

in the other two cases, instead, there is no risk of splitting

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Principals’ decisions in February

Each principal manages three classes (in different schools)

and has to allocate a total of I immigrants

With probability 1− π the class expected to be large in February

will remain large

the principal will not put immigrants in it

immigrants will end up in the other two classes

Therefore,

the February allocation of immigrants across the three classes, is:

Isg =

0 if CN

sg = HI2 if CN

sg = MI2 if CN

sg = L

(4)

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Final allocation in September

The allocation of immigrants based on the final number of natives per

class CNsg , after late enrolment has occurred, is,

Isg =

≈ 0 if CN

sg ≈ HI2 if CN

sg ≈ M

≈ I2

1(1+2π) if CN

sg ≈ L

(5)

The number of immigrants is a hump-shaped function of the final

number of natives per class

some small classes originate from final splitting of classes expected

to be large in February and that were thus without immigrants

classes that remain large have no immigrants

the highest number of immigrants remains allocated to classes with

an intermediate number of natives

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Natives and immigrants in a class as a function of predicted

class size based on native enrolment, pooling grade 2 and 5

1.8

22.

22.

4N

umbe

r of

imm

igra

nts

per

clas

s

1012

1416

1820

Num

ber

of n

ativ

es p

er c

lass

10 15 20 25Theoretical class size based on enroled natives and Maimonides rule

Observed number of natives (avg) Fitted number of nativesObserved number of immigrants (avg) Fitted number of immigrants

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Estimated equation

We apply our identification strategy to equation

Vjskg = α + βNjskg + γIjskg + µXjskg + ηkg + f (Nsg ) + ujskg , (14)

which includes

fixed effects defined at the institution×grade level

a polynomial in native enrolment at the school×grade level

to control for the systematic and continuous components of the

relationship between native enrolment and native performance

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Instruments

Instruments are constructed as Angrist and Lang (2004):

Ψ ∈ {1(1 ≤ CNsg < 2), 1(2 ≤ CN

sg < 3), ...., 1(24 ≤ CNsg < 25}, (15)

They are indicators defined for each possibile level of the theoreticalnumber of natives in a class, CN

sg , predicted by

CNsg =

Nsg

Int(Nsg−1

25

)+ 1

(13)

They capture in the most flexible way the

non-linearities and

discontinuities

generated by the rules of class formation, that relate native enrolmentto the numbers of natives and immigrants in a class

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IV-FE estimates: Language

OLS-FE IV-FE

Number of natives: β 0.0001 -0.0019**(0.0003) (0.0007)

Number of immigrants: γ -0.0049*** -0.0177***(0.0006) (0.0054)

PEC: δ -0.0050*** -0.0158***(0.0006) (0.0052)

Observations 25,943 25,943Institution×grade FE X XPolynomial in natives enrolment XClass level controls X XHansen (p-value) n.a. 0.715

Natives (F-test) n.a. 382.52Natives (AP-test) n.a. 187.98Immigrants (F-test) n.a. 299.19Immigrants (AP-test) n.a. 88.01

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IV-FE estimates: Mathematics

OLS-FE IV-FE

Number of natives: β 0.0002 -0.0010(0.0003) (0.0009)

Number of immigrants: γ -0.0042*** -0.0168***(0.0007) (0.0056)

PEC: δ -0.0044*** -0.0158***(0.0006) (0.0053)

Observations 25,943 25,936Institution×grade FE X XPolynomial in natives enrolment XClass level controls X XHansen (p-value) n.a. 0.972

Natives (F-test) n.a. 221.76Natives (AP-test) n.a. 193.84Immigrants (F-test) n.a. 46.45Immigrants (AP-test) n.a. 40.90

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Analysis by grade

Qualitatively similar results

Sometimes less precise

γ and β typically larger in 5th than 2nd grade

Language: Instrumental Variable estimates by grade

Mathematics: Instrumental Variable estimates by grade

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The threat of test scores manipulation by teachers

Angrist, Battistin and Vuri (2014) find evidence that test scores are

manipulated by teachers in some southern regions of the country

more as a result of shirking than because of self-interested cheating

Our results are essentially unchanged when we restrict the analysis to

different sub-samples in which, according to ABV, score manipulation

is likely to be minimal, if at all present

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IV-FE estimates in the north and centre: Language

Baseline Classes with Externallyspecification cheating monitored

indicator = 0 institutions

Number of natives: β -0.0026*** -0.0022*** -0.0033**(0.0008) (0.0008) (0.0015)

Number of immigrants: γ -0.0155*** -0.0172*** -0.0180**(0.0053) (0.0055) (0.0075)

PEC: δ -0.0129** -0.0149*** -0.0147**(0.0051) (0.0052) (0.0072)

Observations 19,001 18,636 4730Institution×grade FE X X XPolynomial in natives enrolment X X XClass level controls X X XHansen (p-value) 0.373 0.197 0.475Natives (F-test) 243.61 230.40 92.60Natives (AP-test) 130.66 125.43 49.28Immigrants (F-test) 159.90 156.49 13.17Immigrants (AP-test) 58.39 57.49 8.91

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IV-FE estimates in the north and centre: Math

Baseline Classes with Externallyspecification cheating monitored

indicator = 0 institutions

Number of natives: β -0.0008 -0.0010 -0.0019(0.0009) (0.0009) (0.0017)

Number of immigrants: γ -0.0129** -0.0155*** -0.0160*(0.0055) (0.0055) (0.0084)

PEC: δ -0.0121** -0.0145*** -0.0141*(0.0052) (0.0052) (0.0079)

Observations 19,005 18,697 4733Institution×grade FE X X XPolynomial in natives enrolment X X XClass level controls X X XHansen (p-value) 0.878 0.832 0.694Natives (F-test) 165.09 169.27 103.96Natives (AP-test) 137.02 135.53 50.37Immigrants (F-test) 39.65 34.42 14.35Immigrants (AP-test) 33.28 28.70 9.52

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Concluding remarks

Anecdotal evidence of class disruption involving immigrants often

generates concerns in the public opinion and drives policy reactions

We clarify that a useful policy parameter is the PEC effect

the effect of substituing one native with one immigrant in class

net of endogenous principals’ reactions (in numbers and quality)

net of the mechanical class size effects that these inflows entail

The institutional setting in Italy allows us to identify the PEC

Adding one immigrant to a class while taking away one native,

reduces native performance in both language and math

by approximately 1.6%

these estimates are larger than conventional ones because they are

not confounded by principals’ reactions21 / 25

Thank You

Questions and commentsare welcome

You can contact us at

rosariomaria.ballatore@bancaditalia.itmargherita.fort@unibo.it

andrea.ichino@eui.eu

22 / 25

IV-FE estimates: Language

Pooled 2nd grade 5th grade(1) (2) (3)

Number of natives: β -0.0019** -0.0025** -0.0011(0.001) (0.001) (0.001)

Number of immigrants: γ -0.0177*** -0.0150* -0.0182***(0.005) (0.008) (0.006)

(Pure) composition effect: δ -0.0158*** -0.0125 -0.0171**(0.005) (0.008) (0.006)

Observations 25,943 12,859 13,084Institution×grade FE X X XPolynomial in natives enrolment X X XClass level controls X X XHansen (p-value) 0.716 0.717 0.718F test (excluded instruments)Natives 382.52 185.09 231.93Immigrants 299.19 90.97 86.91

Back 23 / 25

IV-FE estimates: Math

Pooled 2nd grade 5th grade(4) (5) (6)

Number of natives: β -0.0010 -0.0013 -0.0005(0.001) (0.001) (0.001)

Number of immigrants: γ -0.0168*** -0.0134 -0.0174**(0.005) (0.008) (0.006)

(Pure) composition effect: δ -0.0158*** -0.0121 -0.0169**(0.005) (0.008) (0.007)

Observations 25,936 12,854 13,082Institution×grade FE X X XPolynomial in natives enrolment X X XClass level controls X X XHansen (p-value) 0.972 0.778 0.866F test (excluded instruments)Natives 221.76 141.52 194.88Immigrants 46.46 48.59 76.97

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Actual and predicted number of natives in a class based on

native enrolment, pooling grade 2 and 510

1520

25

10 25 50 75Natives enrollment in schools

Theoretical class sizeClass size without immigrants

Class size with immigrants

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